Solvent water interacts strongly with polar groups, and hence molecular dynamics simulation of proteins requires a treatment that recognizes the presence of solvent. Explicit treatment of water molecules results in a large increase of scale because a great many water molecules must be used to reproduce the polarization. Also, long simulations are needed to properly average over many water configurations and to reproduce the solvent screening effect on the electrostatic interactions between charged protein atoms. This subproject seeks to develop a continuum dielectric description of water as a polar solvent gives for use in an alternative approach to molecular dynamics simulation of a protein in aqueous solution. From a statistical mechanical point of view, the continuum dielectric model corresponds to averaging over solvent degrees of freedom for each protein conformation. The solvation free energy and the forces exerted by the solvent on the atoms of the protein can be calculated from the solvent reaction field potential, which, in turn is a solution of the Poisson equation for the protein in the dielectric environment, with high dielectric constant outside the volume of the protein atoms and low dielectric constant inside this volume. A successful practical implementation of the continuum-dielectric model into the molecular dynamics method depends on the quality (speed and accuracy) of the solution of the Poisson equation. The well-known DELPHI method (developed by B. Honig's group at Columbia University) for solving the Poisson equation numerically is unacceptable in this case, because the DELPHI method implements the solution on a finite 3-D grid and the mapping on the 3-D grid depends on the grid position and orientation relative to that of the protein molecule. This raises the complicated question of the stability of the solution of the Poisson equation in the presence of translational and rotational motion of the protein and of a change in the protein conformation. The boundary element method presents an alternative method for the numerical solution of the Poisson equation as it is rotationally and translationally invariant and therefore more promising for use in dynamics simulations. At Cornell University Y. Vorobjev and H. Scheraga have developed an adaptive Multigrid Boundary Element method (MBE) for use in macromolecular electrostatic computations in a solvent environment. The MBE method uses an adaptive tessellation of the molecular surface into boundary elements with irregular size, and converts the integral equations of the BE method into numerical linear equations of low dimensionality. Computing time is saved by having the size of the boundary elements increase in three successive levels as the uniformity of the electrostatic field on the molecular surface increases. The results of the MBE method vary relatively little when the size of the boundary elements is varied, and are consistent with results obtained with DELPHI. The MBE method is well suited for use on parallel computers. The current version of the three-level MBE method has been used to calculate the free energy of transfer from vacuum to aqueous solution and the free energy of the equilibrium state of ionization of a 17-residue peptide in a given conformation at a given pH in 400 sec of CPU time on one node of an IBM SP2 supercomputer. The three-level MBE can be generalized into an unrestricted MBE method. The UMBE method provides an optimal adaptive tessellation of the macromolecular surface with the multigrid boundary elements to achieve maximal speed and accuracy of the solution of the Poisson equation. We estimate that the computational effort of the UMBE method scales as O(number of atoms in the macromolecule). There is no obvious limit on the size of macromolecule for which UMBE can be used. We have nearly completed a first version of the code of the UMBE method, which can calculate free energy of solvation and reaction field forces on protein atoms. Tests of the UMBE sequential code with the eglin protein test system give a timing of about 100 sec on the SGI Power Onyx. Calculation of the autocorrelation function for the reaction field forces for the eglin-water system has shown that the forces exerted by the solvent molecules on the protein vary relatively slowly during a molecular dynamics trajectory calcualted with explicit representaitn of solvent molecules. Therefore, the reaction field forces need to be updated only once every 50 to 100 fsec, i.e. once every 50 to 100 dynamics time steps. These preliminary results show that the UMBE method can be incorporated into molecular dynamics code and used to perform large scale molecular dynamics simulation of a protein in aqueous solution, without requiring a large increase in computer time over the same simulation done with explicit water molecules and periodic boundary conditions. Tropsha, O'Connell and Wang)